making tiny edge and gaps
If you want to stay with only one object:

Use bevel tool and extrusion

In Edit mode, after selecting all the edge where your tiny gap will apear, press Ctrl+B you will separate your edge in two edges, you can set the distance between them by moving your mouse or after that using the Amout value in the Bevel menu on the Left of the 3D view.

After that simply extrude the newly created face with E inside your mesh.

If you want to separate your mesh to work withtwo objects :

Separate

Select all the upper part of the phone and press P and select 'Selection'. You will need to do some scale modification to your object.